Acoustics of thunder: A quasilinear model for tortuous lightning

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Abstract
An approximate quasilinear theory of thunder generation by tortuous lightning channels has been developed herein. It was applied to predict the major features of thunder, with details of the rumble and roll; these cannot be accounted for by current nonlinear treatments that exclude tortuosity. The waveform forecast is deterministic for a specific channel configuration and observer location: it is in effect a m a p p i n g o f t h e s h a p e o f l i g h t n i n g i n t o t h e s o u n d o f t h u n d e r. The lightning stroke is modeled as a tortuous line emitting N‐shaped pressure waves from points all along its length. Although emitted simultaneously, they arrive sequentially according to distance: the received pressure signature is essentially a convolution of an N wave with a channel‐shape function. Thus the thunder spectrum approximates a product form: an N‐wave spectrum modulated by another due to channel tortuosity. In computer simulation a lightning channel was approximated as a zig‐zag chain of straight segments; resolution was down to ∼3 m to yield zero‐crossing frequencies of order 200 Hz. Suitable 3‐D shapes were generated, using appropriate deflection probabilities. The computer carried out the integration (here a summation) to produce the thunder pressure signature. With fast D/A, the output (a voltage) varies in real time; it was tape recorded for playback as a u d i b l e synthetic thunder. Other calculations with ‘‘stylized’’ channel shapes showed how specific thunder features correlate one‐to‐one with geometric channel features. The emission from successive collinear segments was found to largely cancel, except as they approach perpendicularity to the sound rays: the latter case yields a focused thunderclap. Conversely, t h e u n c a n c e l e d e m i s s i o n f r o m c o r n e r s o r k i n k s i n a l i g h t n i n g c h a n n e l w a s i d e n t i f i e d a s a m a j o r e l e m e n t i n t h u n d e r e m i s s i o n. The corner effect accounts for the long duration (up to tens of seconds) of a real thunder signature compared with the single short thunderclap predicted for a long straight channel. The tortuous channel thunder predicted by the computermodel was found to be compatible in (i) waveform appearance, (ii) spectral characteristics, and (iii) a u d i b l e sound with real thunder (cf. bound‐in soundsheet).

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